Artificial bee colony algorithm with dynamic population size to combined economic and emission dispatch problem Dog ˘an Aydin a , Serdar Özyön b,⇑ , Celal Yas ßar b , Tianjun Liao c a Computer Engineering Department, Dumlupınar University, 43100 Kütahya, Turkey b Electrical and Electronics Engineering Department, Dumlupınar University, 43100 Kütahya, Turkey c IRIDIA, CoDE, Universite Libre de Bruxelles, Brussels, Belgium article info Article history: Received 24 December 2012 Received in revised form 20 June 2013 Accepted 28 June 2013 Keywords: Combined economic and emission dispatch Weighted sum method Artificial bee colony algorithm Dynamic population size Parameter control abstract Incremental Artificial Bee Colony algorithm with Local Search (IABC-LS) is one of efficient variant of arti- ficial bee colony optimization which was successfully applied to economic power dispatch problems before. However IABC-LS algorithm has some tunable parameters which are directly affecting the algo- rithm behavior. In this study, we have introduced a new algorithm namely Artificial Bee Colony with Dynamic Population size (ABCDP) which is using similar mechanisms defined in IABC-LS without using many parameters to be tuned. To prove the efficiency and robustness of algorithm in power dispatch, the algorithm is used for the combined economic and emission dispatch problem which is converted into single objective optimization problem. For fair comparison, the parameters of both IABC and ABCDP algo- rithms are determined via automatic parameter configuration tool, Iterated F-Race. IEEE 30 bus test sys- tem and 40-generator units problem are used as the problem instances. The results of the algorithms indicate that ABCDP is giving good results in both systems and very competitive with the state-of-the-art. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction Economic dispatch (ED) problem is one of the main subjects of power system operations. The main objective of the ED problem can be explained as meeting the power demand by operating power generation units with the minimum cost while satisfying the equality and inequality constraints of the system. Optimal solution of the ED problem provides significant economic advanta- ges. With the increased interest in environmental pollution, the traditional ED, which ignores the pollutant emissions of the fossil fuels used by the thermal plants, no longer satisfies the needs. Therefore, the environmental economic dispatch (EED), as an alter- native, has become more attractive, because it considers the pollu- tant emissions as well as economic advantages. The solution of the EED problem comprises some important evaluation criteria such as fuel cost, environmental impact and total active power loss. So, the EED problem is a multi-objective mathematical problem in which conflicting objectives are optimized simultaneously [1–5]. In general, the EED problem can be solved by three approaches in the literature [5,6]. In the first approach, the amount of emission is calculated as a constant within the permitted limits. However, it is quite difficult to formulate the trade-off relations between fuel cost and emission. As an example to this approach, the EED prob- lem was solved with Davidon–Fletcher–Powell’s method (DFPM) [7] with the emission amount taken as a constant in the permitted limits. In the second approach, decreasing emission is considered in addition to the cost minimization. In this case, multi objective opti- mization problem in the solution of the EED problem is converted into a single objective optimization problem that considers only one objective at a time or the linear combination of two objectives. In the literature, This type of optimization problem was solved using algorithms such as genetic algorithm [8], differential evolu- tion algorithm (DE) [9], particle swarm optimization algorithm (PSO) [10], artificial bee colony algorithm (ABC) [11], the fast suc- cessive linear programming algorithm (SLP) [12], the evolutionary programming algorithms (EP) [13], the hybrid bacterial foraging Nelder–Mead algorithm (MF–NM) [14], hybrid differential evolu- tion with biogeography-based optimization algorithm (DE/BBO) [15], analytical solution (AS) [16], Newton–Raphson method (NRM) [17], opposition-based gravitational search algorithm (OGSA) [18] and first order gradient method (FOGM) [19]. As for the third approach, simultaneously conflicting objectives are evaluated together in the solution of the EED problem. Both the fuel cost and the emission are minimized together. In the litera- ture, as an example to such an approach, the optimization problem was solved with methods such as multi-objective Mathematical Programming (MMP) formulation based on a fast e-constraint 0142-0615/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijepes.2013.06.020 ⇑ Corresponding author. Tel.: +90 5556261007. E-mail addresses: dogan.aydin@dpu.edu.tr (D. Aydin), serdar.ozyon@dpu.edu.tr (S. Özyön), celal.yasar@dpu.edu.tr (C. Yas ßar), tliao@ulb.ac.be (T. Liao). Electrical Power and Energy Systems 54 (2014) 144–153 Contents lists available at SciVerse ScienceDirect Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes